We report the basic nonlinear optical properties, namely, two-photon absorption coefficient (b), three-photon absorption coefficient (c), and Kerr nonlinear refractive index (n kerr), of GaN crystals in polar c-plane, nonpolar m-plane, and semipolar (2021) plane orientations. A typical Z-scan technique was used for the measurement with a femtosecond Ti:S laser from wavelengths of 724 nm to 840 nm. For the two-photon absorption coefficient (b), similar values were obtained for polar, nonpolar, and semipolar samples, which are characterized to be $0.90 cm/GW at 724 nm and $0.65 cm/GW at 730 nm for all the three samples. For the Kerr nonlinear refractive index (n kerr), self-focusing features were observed in this work, which is different from previous reports where self-defocusing features were observed on GaN in the visible and near-UV spectral regions. At 724 nm, n kerr was measured to be $2.5 0 Â 10 À14 cm 2 =W for all three samples. Three-photon absorption coefficients (c) were also determined, which were found to be consistent with previous reports. This study provides valuable information on the basic nonlinear optical properties of III-nitride semiconductors, which are vital for a wide range of applications such as integrated photonics and quantum photonics.